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Jun 28, 2018
06/18

by
Jürgen Jost

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We review the role of mathematics from a historical and a conceptual perspective in the light of modern data science.

Topics: History and Overview, Mathematics

Source: http://arxiv.org/abs/1510.07172

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Jun 30, 2018
06/18

by
Daniel Jost

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Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative...

Topics: Molecular Networks, Quantitative Biology

Source: http://arxiv.org/abs/1401.2749

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Jun 29, 2018
06/18

by
Jost Migenda

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For detection of neutrinos from galactic supernovae, the planned Hyper-Kamiokande detector will be the first detector that delivers both a high event rate (about one third of the IceCube rate) and event-by-event energy information. In this thesis, we use a three-dimensional computer simulation by the Garching group to find out whether this additional information can be used to improve the detection prospects of fast time variations in the neutrino flux. We find that the amplitude of SASI...

Topics: Instrumentation and Methods for Astrophysics, Physics, Astrophysics, High Energy Astrophysical...

Source: http://arxiv.org/abs/1609.04286

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Sep 18, 2013
09/13

by
Christine Jost

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Recently, Willwacher showed that the Grothendieck-Teichmuller group GRT acts by L-infinity-automorphisms on the Schouten algebra of polyvector fields T_poly(R^d) on affine space R^d. In this article, we prove that a large class of L-infinity-automorphisms on the Schouten algebra, including Willwacher's, can be globalized. That is, given an L-infinity-automorphism of T_poly(R^d) and a general smooth manifold M with the choice of a torsion-free connection, we give an explicit construction of an...

Source: http://arxiv.org/abs/1201.1392v3

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Sep 22, 2013
09/13

by
Celine Jost

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We derive a class of ergodic transformations of self-similar Gaussian processes that are Volterra, i.e. of type X_t = int^t_0 z_X(t,s)dW_s, t>0, where z_X is a deterministic kernel and W is a standard Brownian motion.

Source: http://arxiv.org/abs/math/0702096v2

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Sep 21, 2013
09/13

by
Celine Jost

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We proof a connection between the generalized Molchan-Golosov integral transform and the generalized Mandelbrot-Van Ness integral transform of fractional Brownian motion (fBm). The former changes fBm of arbitrary Hurst index K into fBm of index H by integrating over [0,t], whereas the latter requires integration over (-infty,t].

Source: http://arxiv.org/abs/math/0602356v2

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Sep 21, 2013
09/13

by
Christine Jost

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The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective space. The computations can be done both symbolically and numerically, the latter using an interface to Bertini. We provide some background of the implementation and show how to use the package with the help of examples.

Source: http://arxiv.org/abs/1301.4125v2

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Sep 21, 2013
09/13

by
Christine Jost

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We present an algorithm for the symbolic and numerical computation of the degrees of the Chern-Schwartz-MacPherson classes of a closed subvariety of projective space P^n. As the degree of the top Chern-Schwartz-MacPherson class is the topological Euler characteristic, this also yields a method to compute the topological Euler characteristic of projective varieties. The method is based on Aluffi's symbolic algorithm to compute degrees of Chern-Schwartz-MacPherson classes, a symbolic method to...

Source: http://arxiv.org/abs/1301.4128v3

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Sep 23, 2013
09/13

by
Juergen Jost

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We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic plasticity (\cite{KGvHW,KGvH1,vH}). Our learning rule for the synaptic weight $w_{ij}$ is $$ \dot w_{ij}(t)= \epsilon \int_{-\infty}^\infty \frac{1}{T_l} \int_{t-T_l}^t \sum_\mu \delta(\tau+s-t_{j,\mu}) u(\tau) d\tau\ \Gamma(s)ds $$ where the $t_{j,\mu}$ are the...

Source: http://arxiv.org/abs/q-bio/0511012v1

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Sep 19, 2013
09/13

by
Celine Jost

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We consider Volterra Gaussian processes on [0,T], where T>0 is a fixed time horizon. These are processes of type X_t=\int^t_0 z_X(t,s)dW_s, t\in[0,T], where z_X is a square-integrable kernel, and W is a standard Brownian motion. An example is fractional Brownian motion. By using classical techniques from operator theory, we derive measure-preserving transformations of X, and their inherently related bridges of X. As a closely connected result, we obtain a Fourier-Laguerre series expansion...

Source: http://arxiv.org/abs/math/0701888v2

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Sep 24, 2013
09/13

by
Bobo Hua; Juergen Jost; Xianqing Li-Jost

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In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic functions on lattices $\mathds{Z}^n$ that does not use a representation formula for harmonic functions. We also calculate the precise dimension of the space of polynomial growth harmonic functions on...

Source: http://arxiv.org/abs/1112.6284v3

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Jun 28, 2018
06/18

by
Jost Tobias Springenberg

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In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an...

Topics: Statistics, Learning, Machine Learning, Computing Research Repository

Source: http://arxiv.org/abs/1511.06390

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Jun 30, 2018
06/18

by
Wiktor Młynarski; Jürgen Jost

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Binaural sound localization is usually considered a discrimination task, where interaural time (ITD) and level (ILD) disparities at pure frequency channels are utilized to identify a position of a sound source. In natural conditions binaural circuits are exposed to a stimulation by sound waves originating from multiple, often moving and overlapping sources. Therefore statistics of binaural cues depend on acoustic properties and the spatial configuration of the environment. In order to process...

Topics: Quantitative Biology, Sound, Computing Research Repository, Neurons and Cognition

Source: http://arxiv.org/abs/1402.4648

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Jun 29, 2018
06/18

by
Jost Eschenburg; Bernhard Hanke

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We sketch a geometric proof of the classical theorem of Atiyah, Bott, and Shapiro \cite{ABS} which relates Clifford modules to vector bundles over spheres. Every module of the Clifford algebra $Cl_k$ defines a particular vector bundle over $\S^{k+1}$, a generalized Hopf bundle, and the theorem asserts that this correspondence between $Cl_k$-modules and stable vector bundles over $\S^{k+1}$ is an isomorphism modulo $Cl_{k+1}$-modules. We prove this theorem directly, based on explicit...

Topics: Differential Geometry, Mathematics

Source: http://arxiv.org/abs/1610.04385

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0.0

Jun 29, 2018
06/18

by
Sergio Antoy; Andy Jost

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We introduce a new native code compiler for Curry codenamed Sprite. Sprite is based on the Fair Scheme, a compilation strategy that provides instructions for transforming declarative, non-deterministic programs of a certain class into imperative, deterministic code. We outline salient features of Sprite, discuss its implementation of Curry programs, and present benchmarking results. Sprite is the first-to-date operationally complete implementation of Curry. Preliminary results show that...

Topics: Programming Languages, Computing Research Repository

Source: http://arxiv.org/abs/1608.04016

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Sep 23, 2013
09/13

by
Danijela Horak; Jürgen Jost

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The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies eigenvalue bounds for the other one. In this paper, we therefore develop topological arguments in order to de- rive such analytical inequalities. We investigate, in a general and systematic manner, interlacing of spectra for weighted simplicial complexes with...

Source: http://arxiv.org/abs/1111.1836v2

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Jul 20, 2013
07/13

by
Hannah Arendt; Jorgensen Jost

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In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if and only if they coincide on a node at the same time. We conduct numerical study on the consensus problem in this framework and show that global consensus can be achieved.

Source: http://arxiv.org/abs/1203.1900v1

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Jul 20, 2013
07/13

by
Nora Touati; Vincent Jost

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The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.

Source: http://arxiv.org/abs/1203.1604v1

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Sep 20, 2013
09/13

by
Juergen Jost; Wei Li

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We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of them pushes too hard, no deal at all can be concluded, and they both loose. The game has many equilibria, and which of them is reached depends on the history of the interactions as the players evolve according to a fitness function that measures their gains...

Source: http://arxiv.org/abs/nlin/0405012v2

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Sep 19, 2013
09/13

by
Juergen Jost; Kang Zuo

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We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis, we can investigate the relation between the properties of the original representation and what can be inferred by restricting it to the fibers of a fibration.

Source: http://arxiv.org/abs/math/0010296v1

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Sep 22, 2013
09/13

by
Guyslain Naves; Vincent Jost

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We are given a graph $G$, an independant set $\mathcal{S} \subset V(G)$ of \emph{terminals}, and a function $w:V(G) \to \mathbb{N}$. We want to know if the maximum $w$-packing of vertex-disjoint paths with extremities in $\mathcal{S}$ is equal to the minimum weight of a vertex-cut separating $\mathcal{S}$. We call \emph{Mader-Mengerian} the graphs with this property for each independant set $\mathcal{S}$ and each weight function $w$. We give a characterization of these graphs in term of...

Source: http://arxiv.org/abs/1101.2061v1

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Sep 23, 2013
09/13

by
Danijela Horak; Jürgen Jost

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We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the weighted Laplacian, and the normalized graph Laplacian. This framework then allows us to define the normalized Laplace operator $\Delta_{i}^{up}$ on simplicial complexes which we then systematically investigate. We study the effects of a wedge sum, a join and...

Source: http://arxiv.org/abs/1105.2712v3

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Sep 18, 2013
09/13

by
Juergen Jost; Guofang Wang

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We consider solutions of a Toda system for SU(N+1) and show that any solution with finite exponential integral cam be obtained from a rational curve in complex projective space of dimension N

Source: http://arxiv.org/abs/math-ph/0105045v1

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Sep 23, 2013
09/13

by
Wenyi Chen; Juergen Jost

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We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev $H^{2,2}$-norm of such a map in terms of its energy, the $L^2$-norm of its tension field and a topological term depending on the homotopy class. We also solve a Dirchlet problem without an underlying variational structure, as an extension of the topic of harmonic maps with potentials.

Source: http://arxiv.org/abs/math/0312233v1

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Sep 19, 2013
09/13

by
Dominic Jost; Kai Nagel

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There is discussion if traffic displays multiple phases (e.g. laminar, jammed, synchronized) or not. This paper presents evidence that a stochastic car following model, by changing one of its parameters, can be moved from showing two phases (laminar and jammed) to showing only one phase. Models with two phases show three states: two being homogeneous states corresponding to each phase, and a third state which consists of a mix between the two phases (phase coexistence). Although the gas-liquid...

Source: http://arxiv.org/abs/cond-mat/0208082v1

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Sep 23, 2013
09/13

by
Juergen Jost; Yuanlong Xin

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The first Betti number for a lattice in a classifying space for variations of Hodge structures vanishes.

Source: http://arxiv.org/abs/math/0312146v1

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Sep 21, 2013
09/13

by
Juergen Jost; Wei Li

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We study a complementarity game with multiple populations whose members' offered contributions are put together towards some common aim. When the sum of the players' offers reaches or exceeds some threshold K, they each receive K minus their own offers. Else, they all receive nothing. Each player tries to offer as little as possible, hoping that the sum of the contributions still reaches K, however. The game is symmetric at the individual level, but has many equilibria that are more or less...

Source: http://arxiv.org/abs/1011.3666v1

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Sep 18, 2013
09/13

by
Anirban Banerjee; Jürgen Jost

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From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary dynamics leading to those particular data can then be developed. This method is exemplified for protein-protein interaction networks. Traces of their evolutionary history of duplication and divergence processes are identified. In particular, we can identify typical...

Source: http://arxiv.org/abs/0705.3373v1

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Sep 23, 2013
09/13

by
Juergen Jost; Yihu Yang

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The fundamental group of a Riemannian manifold with $\delta$-pinched negative curvature, $\delta >1/4$, cannot be the fundamental group of a quasicompact K\"ahler manifold. The proof also implies that a non-uniform lattice in $F_{4(-20)}$ cannot be the fundamental group of a quasicompact K\"ahler manifold. We also construct examples in the spirit of Gromov-Thurston to show that our result is a non-trivial extension of the previously known result that a non-uniform lattice in real...

Source: http://arxiv.org/abs/math/0312143v1

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Sep 21, 2013
09/13

by
Hao Chen; Jürgen Jost

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We present here another proof of Oscar Rojo's theorems about the spectrum of graph Laplacian on certain balanced trees, by taking advantage of the symmetry properties of the trees in question, and looking into the eigenfunctions of Laplacian.

Source: http://arxiv.org/abs/1011.3361v1

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Sep 22, 2013
09/13

by
Juergen Jost; Guofang Wang

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We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality

Source: http://arxiv.org/abs/math-ph/0011039v1

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Sep 23, 2013
09/13

by
Huijun Fan; Juergen Jost

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We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distinguished from general flows carrying a cocycle by boundedness conditions on these integrals.

Source: http://arxiv.org/abs/math/0312018v1

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Sep 19, 2013
09/13

by
Frank Bauer; Jürgen Jost

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We study the spectrum of the normalized Laplace operator of a connected graph $\Gamma$. As is well known, the smallest nontrivial eigenvalue measures how difficult it is to decompose $\Gamma$ into two large pieces, whereas the largest eigenvalue controls how close $\Gamma$ is to being bipartite. The smallest eigenvalue can be controlled by the Cheeger constant, and we establish a dual construction that controls the largest eigenvalue. Moreover, we find that the neighborhood graphs $\Gamma[l]$...

Source: http://arxiv.org/abs/0910.3118v4

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Sep 19, 2013
09/13

by
J. Jost; L. Todjihounde

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We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric process that converges to such maps, called harmonic nets for short.

Source: http://arxiv.org/abs/0708.2806v1

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Sep 21, 2013
09/13

by
Anirban Banerjee; Jürgen Jost

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We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or duplication leave characteristic traces in the spectrum. This can suggest hypotheses about the evolution of a graph representing biological data. To this data, we analyze several biological networks in terms of rough qualitative data of their spectra.

Source: http://arxiv.org/abs/0706.0113v1

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Sep 19, 2013
09/13

by
Huijun Fan; Juergen Jost

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The present paper contains an interpretation and generalization of Novikov's theory of Morse type inequalities for 1-forms in terms of Conley's theory for dynamical systems.

Source: http://arxiv.org/abs/math/0010295v1

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Sep 19, 2013
09/13

by
Hao Chen; Jürgen Jost

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We show that, in the graph spectrum of the normalized graph Laplacian on trees, the eigenvalue 1 and eigenvalues near 1 are strongly related to minimum vertex covers. In particular, for the eigenvalue 1, its multiplicity is related to the size of a minimum vertex cover, and zero entries of its eigenvectors correspond to vertices in minimum vertex covers; while for eigenvalues near 1, their distance to 1 can be estimated from minimum vertex covers; and for the largest eigenvalue smaller than 1,...

Source: http://arxiv.org/abs/1010.4269v5

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Sep 22, 2013
09/13

by
Jürgen Jost; Shiping Liu

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In Riemannian geometry, Ricci curvature controls how fast geodesics emanating from a common source are diverging on average, or equivalently, how fast the volume of distance balls grows as a function of the radius. Recently, such ideas have been extended to Markov processes and metric spaces. Employing a definition of generalized Ricci curvature proposed by Ollivier and applied in graph theory by Lin-Yau, we derive lower Ricci curvature bounds on graphs in terms of local clustering...

Source: http://arxiv.org/abs/1103.4037v2

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Sep 21, 2013
09/13

by
Anirban Banerjee; Jürgen Jost

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It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize...

Source: http://arxiv.org/abs/0706.1198v1

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Sep 23, 2013
09/13

by
Juergen Jost; Yihu Yang

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We deform a map into a Riemannian manifold that is horizontal with respect to a submersion onto a non-positively curved manifold and satisfies a Chow condition into a harmonic one through a horizontal homotopy.

Source: http://arxiv.org/abs/math/0312144v1

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Sep 21, 2013
09/13

by
Bobo Hua; Juergen Jost

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We prove an analogue of Yau's Caccioppoli-type inequality for nonnegative subharmonic functions on graphs. We then obtain a Liouville theorem for harmonic or non-negative subharmonic functions of class Lq, 1

Source: http://arxiv.org/abs/1301.3403v1

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Sep 18, 2013
09/13

by
Anirban Banerjee; Jürgen Jost

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The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling, graph joining or splitting. The eigenvalue 1 plays a particular role, and we therefore emphasize those constructions that change its multiplicity in a controlled manner, like the iterated duplication of...

Source: http://arxiv.org/abs/0705.3772v1

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Sep 18, 2013
09/13

by
Bobo Hua; Juergen Jost

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We consider harmonic functions of polynomial growth of some order $d$ on Cayley graphs of groups of polynomial volume growth of order $D$ w.r.t. the word metric and prove the optimal estimate for the dimension of the space of such harmonic functions. More precisely, the dimension of this space of harmonic functions is at most of order $d^{D-1}$. As in the already known Riemannian case, this estimate is polynomial in the growth degree. More generally, our techniques also apply to graphs roughly...

Source: http://arxiv.org/abs/1201.5238v2

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Sep 24, 2013
09/13

by
Bobo Hua; Juergen Jost

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In a previous paper Hua-Jost-Liu, we have applied Alexandrov geometry methods to study infinite semiplanar graphs with nonnegative combinatorial curvature. We proved the weak relative volume comparison and the Poincar\'e inequality on these graphs to obtain an dimension estimate of polynomial growth harmonic functions which is asymptotically quadratic in the growth rate. In the present paper, instead of using volume comparison on graphs, we directly argue on Alexandrov spaces to obtain the...

Source: http://arxiv.org/abs/1112.6282v3

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Sep 21, 2013
09/13

by
Juergen Jost; Wei Li

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We study a complementarity game as a systematic tool for the investigation of the interplay between individual optimization and population effects and for the comparison of different strategy and learning schemes. The game randomly pairs players from opposite populations. The game is symmetric at the individual level, but has many equilibria that are more or less favorable to the members of the two populations. Which of these equilibria then is attained is decided by the dynamics at the...

Source: http://arxiv.org/abs/1011.3674v1

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Jun 29, 2018
06/18

by
Lizhen Ji; Juergen Jost

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We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that induce a Riemannian metric and a finite volume measure on each stratum. Applications to the Plateau-Douglas problem for minimal surfaces of varying genus and to the partition function of Bosonic string theory are outlined. The construction starts with a...

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1611.08732

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Sep 19, 2013
09/13

by
Jürgen Jost; Xianqing Li-Jost; Qiaoling Wang; Changyu Xia

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We study eigenvalues of polyharmonic operators on compact Riemannian manifolds with boundary (possibly empty). In particular, we prove a universal inequality for the eigenvalues of the polyharmonic operators on compact domains in a Euclidean space. This inequality controls the $k$th eigenvalue by the lower eigenvalues, independently of the particular geometry of the domain. Our inequality is sharper than the known Payne-P\'olya-Weinberg type inequality and also covers the important Yang...

Source: http://arxiv.org/abs/0910.2067v1

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Sep 19, 2013
09/13

by
Jürgen Jost; Xianqing Li-Jost; Qiaoling Wang; Changyu Xia

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We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.

Source: http://arxiv.org/abs/0910.2063v1

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Sep 18, 2013
09/13

by
Juergen Jost; Yuan-Long Xin

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We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.

Source: http://arxiv.org/abs/math/0101131v1

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Sep 22, 2013
09/13

by
M. Jost; K. D. Usadel

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We study the kinetic roughening of a driven domain wall between spin-up and spin-down domains for a model with non-conserved order parameter and quenched disorder. To understand the scaling behavior of this interface we construct an equation of motion and study it theoretically.

Source: http://arxiv.org/abs/cond-mat/9612015v1